List questions from matrix-rank

Published on 23 Feb 2026 - 10:43

151

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Find linearly dependent rows/columns of rank deficient matrix

Published on 02 Apr 2026 - 1:03

50

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Proof of a property of the inner rank of a matrix.

Published on 13 Feb 2022 - 13:24

27

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Do we always have $\mathcal{R}(A'BA) = \mathcal{R}(A'B)$?

Published on 13 Feb 2022 - 15:06

81

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If $A_{n\times m}B_{m\times k}=0$ then $rk(A)+rk(B)\leq m$

Published on 13 Feb 2022 - 16:49

55

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Does rank $m$ $m \times n$ matrix imply matrix of last $m$ columns is invertible?

Published on 14 Feb 2022 - 1:03

32

Views

Upper bound for $\mathrm{tr}\Big((P + I)^{-1}(P + d uu^T)(P + I)^{-1}\Big)$

Published on 03 Apr 2026 - 16:53

123

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Rank of a $2 \times 2$ block matrix

Published on 29 Mar 2026 - 10:48

38

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Solve for $x$ so that the rank of the matrix is $2$

Published on 16 Feb 2022 - 12:13

35

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Computation of row echelon form of matrix including trigonometric functions

Published on 16 Feb 2022 - 19:35

20

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Construct an invertible $4 \times 4$ block matrix with prescribed invertible sub matrices

Published on 24 Feb 2022 - 17:35

390

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For which values of $a$ will this matrix system fail to have 3 pivots?

Published on 24 Feb 2022 - 20:43

231

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Find $\alpha$ such that $b$ is in the column space of $A$

Published on 25 Feb 2022 - 15:52

39

Views

Intersection of (affine) hyperplanes

Published on 27 Feb 2022 - 12:58

266

Views

when does $\operatorname{rank}(AB)=\operatorname{rank}(A)$?

Published on 01 Mar 2022 - 14:36

List Question

Matrix-rank nonincreasing unitary tensor operations

Find linearly dependent rows/columns of rank deficient matrix

Proof of a property of the inner rank of a matrix.

Do we always have $\mathcal{R}(A'BA) = \mathcal{R}(A'B)$?

If $A_{n\times m}B_{m\times k}=0$ then $rk(A)+rk(B)\leq m$

Does rank $m$ $m \times n$ matrix imply matrix of last $m$ columns is invertible?

Upper bound for $\mathrm{tr}\Big((P + I)^{-1}(P + d uu^T)(P + I)^{-1}\Big)$

Rank of a $2 \times 2$ block matrix

Solve for $x$ so that the rank of the matrix is $2$

Computation of row echelon form of matrix including trigonometric functions

Construct an invertible $4 \times 4$ block matrix with prescribed invertible sub matrices

For which values of $a$ will this matrix system fail to have 3 pivots?

Find $\alpha$ such that $b$ is in the column space of $A$

Intersection of (affine) hyperplanes

when does $\operatorname{rank}(AB)=\operatorname{rank}(A)$?

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